Like Syd said, I used Shadow Lugia during the late-game battles. I didn't have many shadow Pokemon on my team because they cannot gain levels. Shadow Lugia was the star of the team since it can take a hit and dish out damage.

I felt like Lugia wasn't nearly as interesting nor powerful once purified. When I eventually did that, it had a Bashful nature. I wanted something a little better, so in my second playthrough... I got a Bashful Lugia again. D: Screw that, let's just go to Navel Rock. :P caught a shiny Bashful Lugia